Fuzzy Jaccard with Degree of Optimism Ranking Index Based on Function Principle Approach

Jaccard index similarity measure which applies the extension principle approach to obtain fuzzy maximum and fuzzy minimum has been proposed in ranking fuzzy numbers. However, the extension principle used is only applicable to normal fuzzy numbers and, therefore, fails to rank non-normal ones. Apart from that, the extension principle does not preserve the type of membership function of fuzzy numbers and also involves laborious mathematical operations. In this paper, a simple vertex fuzzy arithmetic operation, namely the function principle is applied. This paper also proposes the degree of optimism concept in aggregating the fuzzy evidence. The method is capable to rank both normal and non-normal fuzzy numbers in a simpler manner from all decision makers’ perspectives.